 6.9.1E: The article "Wastewater Treatment Sludge as a Raw Material for the ...
 6.9.2E: The thicknesses of eight pads designed for use in aircraft engine m...
 6.9.3E: The article "Reaction Modeling and Optimization Using Neural Networ...
 6.9.4E: The article "Abyssal Peridotites > 3,800 Ma from Southern West Gree...
 6.9.5E: This exercise shows that the signedrank test can be used with pair...
 6.9.6E: The article "nNonane Hydroconversion on Ni and Pt Containing HMFI,...
 6.9.7E: A new postsurgical treatment is being compared with a standard trea...
 6.9.8E: In an experiment to determine the effect of curing time on compress...
 6.9.9E: In a comparison of the effectiveness of distance learning with trad...
 6.9.10E: A woman who has moved into a new house is trying to determine which...
Solutions for Chapter 6.9: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists  4th Edition
ISBN: 9780073401331
Solutions for Chapter 6.9
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Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Alternative hypothesis
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

Attribute
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

C chart
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defectsperunit or U chart.

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Cook’s distance
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.

Counting techniques
Formulas used to determine the number of elements in sample spaces and events.

Covariance matrix
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the offdiagonal elements are the covariances between Xi and Xj . Also called the variancecovariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

Defect
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

Dispersion
The amount of variability exhibited by data

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

Error of estimation
The difference between an estimated value and the true value.

Exponential random variable
A series of tests in which changes are made to the system under study

False alarm
A signal from a control chart when no assignable causes are present

Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.

Forward selection
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

Harmonic mean
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .